Determine whether the function f(x)= \frac{1}{x} satisfies the two conditions of Mean Value Theorem on the interval [1, 4]. If it does, find all possible values of c such that f'(c)(4-1)=f(4)-f(1) Consider the following limits: \displaystyle \lim_{x \to \frac{ \pi }{2} } (tan x- \frac{2xsecx}{ \pi}) \displaystyle \lim_{x \to 0} ( \frac{xe^x-log(1+x)}{x^2}) \displaystyle\lim_{x\to\infty }{\left( {1 +\frac{5}{x}} ight)^x} \displaystyle \lim_{x \to 0} ( \frac{log(1+kx^2)}{1-cosx}) \displaystyle \lim_{x \to 1}(x^2-1)tan( \frac{\pi x}{2}) Identify the indeterminate forms for each part (I-V) of question 3 above and provide a detailed demonstration. Evaluate each part (I-V) of question 3 above using L'Hpital's Rule and show the calculations at each step